For \(q=4\) , Table REF  gives the distribution of joint counts of the \(105^2=11025\)  pairings \((\sigma ,\tau )\) , among the \(5^3=125\)  possible trivariate types. Those counts have, for lack of foreseeable analytical approach,
been mechanically computed with the help of the R package igraph [1]}, by the functions union() (determining the join of two pairings coded as binary graphs) and components() (determining the join type).
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